四旋翼无人机在SE中的力控制研究(3)

Vicente Parra‐Vega, A. Sanchez, Carlos Izaguirre
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引用次数: 6

摘要

针对四旋翼飞行器受约束欠驱动的位置和姿态动力学模型,即考虑接触扳手,提出了基于弹簧接触力模型的两种新型无模型二阶滑模控制器。利用SE(3)中的解,主要定理建立了闭环系统在零偏航下保证位置和容许接触力的半全局指数跟踪和鲁棒跟踪的条件。在基于四元数的滑动曲面上证明了它是一个对所有时间和任何初始条件的积分滑动模态。这在位置控制方面产生了期望角速度的因果和解析计算,而不涉及状态的导数。导出了具有期望有限时间收敛的终端稳定性的第二个定理。这反过来产生三个结果:a)在适当且易于满足初始化的情况下无奇点表示;B)自由飞行到约束运动的稳定过渡;c)角跟踪误差有限时间收敛的虚拟位置控制器的实现。值得注意的是,对于沿欠驱动方向的力相互作用存在明显的物理限制:沿欠驱动轴的相互作用力越大,需要的滚转和俯仰角越多,可以产生的推力越小,以维持无人机在空中。在各种飞行条件下进行了全面的仿真研究,最后简要讨论了基于微分代数模型的显式(主动)力控制问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Toward force control of a quadrotor UAV in SE(3)
Two novel model-free second order sliding mode controllers are proposed for the constrained underactuated position and orientation dynamic model of the quadrotor, i.e., considering contact wrench, based on spring-like contact force model. The main theorem establishes conditions for the closed-loop system to guarantee semi-global exponential and robust tracking of position and admissible contact forces, with zero yaw, by exploiting the solution in SE(3). It is proved an integral sliding mode for all time and for any initial condition at a quaternion-based sliding surface. This yields a causal and analytical computation of desired angular velocity in terms of position control, without involving derivatives of the state. A second theorem is derived for terminal stability with desired finite time convergence. This in turns produces three results, a) a singularity-free representation under proper and easy to meet initialization; b) stable transition from free flying to constrained motion, and c) realization of the virtual position controller due to finite time convergence of angular tracking errors. It is noted that there arises an evident physical limit for force interaction along underactuated directions: the more interaction force along the underactuated axes, the more roll and pitch angles are needed the less thrust that can be produced to sustain the UAV in the air. Comprehensive simulation study is discussed under various flying conditions, and finally, the explicit (active) force control, based on a differential algebraic model, is briefly addressed.
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